A290036 Number of set partitions of [n] having exactly seven blocks of size > 1.

135135, 6756750, 186486300, 3765521760, 62239847670, 893865232260, 11567184248620, 138167790320560, 1549369653596765, 16513475306458130, 168849390493503720, 1668236066705023200, 16016472213542100300, 150103132298249730600, 1378211903535510443400

Offset: 14

Author

Alois P. Heinz, Jul 18 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 14..1000
• Wikipedia, Partition of a set
• Index entries for linear recurrences with constant coefficients, signature (120, -6930, 256564, -6843837, 140161164, -2293167668, 30793317984, -346027498674, 3301174490432, -27034426023228, 191677191769368, -1184495927428914, 6413285791562760, -30547549870770240, 128399094121475760, -477325107218885805, 1571764443755152680, -4588173158058601250, 11875425392771515860, -27240699344951953809, 55318442559624109580, -99273350219483495580, 157041371328829338576, -218253110396224153888, 265336916554318663296, -280638192440433919872, 256449901319079809536, -200704456428999204096, 133025721255740648448, -73584771640934648832, 33313567375875428352, -12012672014150270976, 3315383509586411520, -657169361790566400, 83234996748288000, -5056584744960000).

Crossrefs

Column k=7 of A124324.

Cf. A290035.

Formula

E.g.f.: (exp(x)-x-1)^7/7!*exp(x).

G.f.: -(1865750631174144*x^21 -13945050326997504*x^20 +49328717299610112*x^19 -109804126032508544*x^18 +172501534253023360*x^17 -203317256909646880*x^16 +186573768183915112*x^15 -136528527507974140*x^14 +80943939197055550*x^13 -39285221171765415*x^12 +15705856242821360*x^11 -5186986300225730*x^10 +1414798298063150*x^9 -317670047760065*x^8 [phone]*x^7 -8663283789160*x^6 [phone]*x^5 -94030401465*x^4 [phone]*x^3 -312161850*x^2 +9459450*x -135135)*x^14 / ((8*x-1) *(7*x-1)^2 *(6*x-1)^3 *(5*x-1)^4 *(4*x-1)^5 *(3*x-1)^6 *(2*x-1)^7 *(x-1)^8).

a(0) = a(1) = 0, for n>1 a(n) = 8*a(n-1) + (n-1)*A290035(n-2). - Ray Chandler, Jul 21 2017